It's just what it sounds like! The Society that Magi made to combine their efforts and police themselves. Since normal people can't know anything about magic, it pretty much had to be made. Some call it the Magus Association, too... the names are basically interchangeable.

Although, not all Magi are part of the Society, for various reasons. I'm not, since the Einzberns are such an old family that they're kind of a law unto themselves.